The Great Schism of 1054 was a very big deal, particularly with regard to major disagreements in Church Doctrine and institutional power.
The main disagreement which led to a "Schism" between the Roman rite and Eastern rite Churches, was the concept of the Trinity. If my memory is correct, the Roman Catholic Church's position was (and is), that the Holy Spirit emanated from "the Father and Son", whereas in the Eastern Church, the Holy Spirit emanated from only "the Father". (One may want to check Wikipedia for further specification. Thomas Aquinas wrote on the Trinity in his "Summa Theologica", though I don't know if he provided any detailed discussion on The Great Schism of 1054 and the Eastern rite Church).
There were many other differences which distinguished and continue to distinguish the Roman rite and Eastern rite Churches which culminated with The Great Schism. The range of theological and institutional differences included (and still include):
The appropriate way of crossing one's self.
The displaying of statues and three dimensional artworks in the Roman Church versus the displaying of icons (and forbidding the display of statues and three dimensional artworks) in the Eastern Church.
The use of the Latin language in the Roman rite Church versus the use of Greek language in the Eastern rite Church-(as well as allowing other Eastern rite Churches to use their own language during Church services, also known as the autocephalic system).
The different interpretations of "Apostolic succession", (as well as the veneration of certain Saints).
In the Roman rite Church, Saint Peter was and is still viewed, as the true heir to Jesus Christ, whereas in the Eastern rite Church, Saint Andrew was and is still viewed, as the true heir to Jesus Christ-(incidentally, both Saints Andrew and Peter were brothers). Peter, was "martyred" in Rome, whereas his brother Andrew, was "martyred" in Greece. Apparently, the geographical location of these two "martyred" Saints reinforced-(and still reinforces), the primacy of each of these Churches' self-identifying lines of "Apostolic succession".
While there were up and down relations between Papal Rome and Constantinople since The Great Schism, as well as the growing Venetian and Genoese presence within many parts of Greece during the late Middle Ages and a Greek expat community, largely from Constantinople, who resettled in Venice and the Veneto during Ottoman imperial expansion towards the West, the Theological differences between the Roman Christian West and the Greek Christian East were (and are still), quite significant; and much of that is directly attributable to the Great Schism of 1054.